例子：

import torch

x = torch.arange(4.0)
x

tensor([0., 1., 2., 3.])

x.requires_grad_(True) # x = torch.arange(4.0, requires_grad=True)
x.grad

y = 2 * torch.dot(x, x)
y

tensor(28., grad_fn=<MulBackward0>)

y.backward()
x.grad

tensor([ 0.,  4.,  8., 12.])

x.grad == 4 * x

tensor([True, True, True, True])

x.grad.zero_()
y = x.sum()
y.backward()
x.grad

tensor([1., 1., 1., 1.])

x.grad.zero_()
y = x * x
y.sum().backward()
x.grad

tensor([0., 2., 4., 6.])

x.grad.zero_()
y = x * x
u = y.detach()
z = u * x

z.sum().backward()
x.grad == u

tensor([True, True, True, True])

x.grad.zero_()
y.sum().backward()
x.grad == 2 * x

tensor([True, True, True, True])

def f(a):
  b = a * 2
  while b.norm() < 1000:
    b = b * 2
  if b.sum() > 0:
    c = b
  else:
    c = 100 * b
  return c

a = torch.randn(size=(), requires_grad=True)
d = f(a)
d.backward()

a.grad == d / a

tensor(True)

bb = torch.arange(4.0)
print(bb)
bbn = bb.norm()
print(bbn)

tensor([0., 1., 2., 3.])
tensor(3.7417)

norm() 函数表示每个数字的平方之和 开根号 (0 ** 2 + 1 ** 2 + 2 ** 2 + 3 ** 2) ^(1/2)

参考

https://www.bilibili.com/video/BV1KA411N7Px